A 2.25 mole sample of helium, which we will assume behaves as a monatomic ideal gas, is expanded under isothermal conditions at constant external pressure Pext from a volume of 4.50 L and a temperature of 298 K to a final volume of 32.5 L. The constant external pressure Pext is chosen, among the various possible options, as the one that results in the most work being done by the gas.

Required:
For this choice, calculate Pext and w.